Targeted radionuclide therapy is a highly efficient but still underused treatment modality for various types of cancers that uses so far mainly readily available β-emitting radionuclides. By using α-particle emitters several shortcomings due to hypoxia, cell proliferation and in the selected treatment of small volumes such as micrometastasis could be overcome. To enable efficient targeting longer-lived α-particle emitters are required. These are the starting point of decay chains emitting several α-particles delivering extremely high radiation doses into small treatment volumes. However, as a consequence of the α-decay the daughter nuclides receive high recoil energies that cannot be managed by chemical radiolabelling techniques. By safe encapsulation of all α-emitters in the decay chain in properly sized nanocarriers their release may be avoided. The encapsulation of small core nanoparticles loaded with the radionuclide in a shell structure that safely confines the recoiling daughter nuclides promises good tumour targeting, penetration and uptake, provided these nanostructures can be kept small enough. A model for spherical nanoparticles is proposed that allows an estimate of the fraction of recoiling α-particle emitters that may escape from the nanoparticles as a function of their size. The model treats the recoil ranges of the daughter nuclides as approximately equidistant steps with arbitrary orientation in a three-dimensional random walk model. The presented model allows an estimate of the fraction of α-particles that are emitted from outside the nanoparticle when its size is reduced below the radius that guarantees complete confinement of all radioactive daughter nuclides. Smaller nanoparticle size with reduced retention of daughter radionuclides might be tolerated when the effects can be compensated by fast internalisation of the nanoparticles by the target cells.

中文翻译：

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一种随机游走方法，用于估计用于靶向放射性核素治疗的纳米粒子中 α 粒子发射器的限制。

靶向放射性核素治疗是一种高效但仍未得到充分利用的治疗方式，适用于各种类型的癌症，迄今为止主要使用现成的β发射放射性核素。通过使用 α 粒子发射器，可以克服由于缺氧、细胞增殖和小体积选择性治疗（例如微转移）而导致的几个缺点。为了实现有效瞄准，需要寿命较长的 α 粒子发射器。这些是衰变链的起点，发射多个α粒子，将极高的辐射剂量传递到小治疗体积中。然而，由于 α 衰变，子核素会受到高反冲能量，而化学放射性标记技术无法控制这种能量。通过将衰变链中的所有α发射体安全封装在适当尺寸的纳米载体中，可以避免它们的释放。将载有放射性核素的小核心纳米颗粒封装在壳结构中，安全地限制反冲子体核素，只要这些纳米结构可以保持足够小，就能实现良好的肿瘤靶向、渗透和吸收。提出了一种球形纳米粒子模型，该模型可以估计可能从纳米粒子中逸出的反冲 α 粒子发射器的分数，作为其尺寸的函数。该模型将子核素的反冲范围视为三维随机游走模型中具有任意方向的近似等距步长。所提出的模型可以估计当纳米粒子的尺寸减小到保证完全限制所有放射性子体核素的半径以下时从纳米粒子外部发射的α粒子的分数。当可以通过靶细胞对纳米颗粒的快速内化来补偿其影响时，可以容忍较小的纳米颗粒尺寸以及子体放射性核素的保留减少。